How can I tell if I can control an application by Applescript?

The easiest thing to do is drag the application's icon on to your script editor (Script Editor, Script Debugger, Smile, etc). In this case you would get a message saying the dictionary could not opened because it has no dictionary and, therefore, doesn't understand AppleScript commands. It is not scriptable. Dragging, say, the Finder onto it will reveal a rich dictionary of commands it understands.

Another technique is to launch your script editor and choose its "Open Dictionary" command, and you will be prompted to choose an application from a list. This practice, however, is not very recommendable these days, when you can waste even minutes waiting for the related list.

Anyway, if the application is not scriptable, you can still attempt to control it via GUI scripting (see "How can I script an application in OS X that isn't scriptable?" in this section).